Try it and see if it works.
Personally, I'd say no. It's better to devote yourself to one, maybe two things, and get really good at those things. Obviously, once you reach a certain level in sports, you're gonna have to train outside of your sport (ie, weightlifting for...most sports) to improve, but the only way to become really good at a sport is to devote yourself to it.
At the same time, when you're younger, you should try out a lot of sports and see what you like, and don't like. You might end up hating football, loving soccer, vice versa, so you gotta try and find out and see what you like. But the problem is, you have to settle down and devote yourself to one sport, or else you're gonna get too flustered trying to train 4 sports at a time.
EDIT:
Familiarity? Oh, you mean...with people? Like social implications of it? Uhm, I'd say doing too many sports would possibly make you seem a bit too much like a "wannabe" if that makes any sense. People don't really like "wannabes."